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Temporal dynamics of morphogen-driven signalling events are critical for proper embryonic development. During development, cells translate extracellular bone morphogenetic protein (BMP) gradients, often subject to noise, into graded intracellular tail-phosphorylated SMAD (TP-SMAD) levels. Using modelling and experimental approaches, we found that BMPs induce TP-SMAD responses in neural precursor cells in a concentration-dependent manner, which are semi-adaptive within a specific intermediate range of BMP concentration. These semi-adaptive TP-SMAD responses involve an intrinsically slow deactivation of BMP receptors, which attenuates noise by prolonging SMAD deactivation time after BMP withdrawal, but increases response time. Interestingly, negative feedback on BMP receptors is also required for semi-adaptation, which benefits both noise attenuation and response time, and therefore balances the trade-off seen with slow BMP receptor deactivation. These results highlight the rich dynamics of SMAD regulation in response to graded BMP concentration, and elucidate general design principles for balancing noise attenuation and activation speed in signalling systems.

Semi-adaptive response and noise attenuation in bone morphogenetic protein signalling